By courting senators and shaping public opinion, the president thinks he can pressure lower-chamber Republicans to accept bipartisan compromises.

On a dreary, drizzly Monday this week, President Obama played golf with three U.S. senators—two Republicans and one Democrat. The outing was the latest in a personal-outreach offensive that has seen Obama schmooze with almost half the Senate—49 members and counting—over dinner or on the fairways. “He’s looking for partners anywhere he can find them, including on the eighth hole,” White House spokesman Jay Carney said.

Anywhere, that is, except the House Republican Conference.

For all the hoopla, the president’s social calendar—the golfing, the steak dinners, the peach-pie desserts—has been reserved almost exclusively for the Senate. It’s a reflection of a White House calculation that Obama must muscle through his ambitious 2013 agenda by charming his way to a supermajority in the upper chamber first, and then use the momentum of an accord and his political operation to bring in line the recalcitrant House. In other words, it’s the inside game in the Senate and, if that works, the outside game in the House.

It is the same playbook that succeeded during the fiscal-cliff crisis when the Senate adopted a bipartisan package, in a deal struck between Vice President Joe Biden and Senate GOP Leader Mitch McConnell, that included tax increases on the rich that the House then reluctantly had to swallow. The White House hopes for a repeat on immigration and, potentially, a major deficit-reduction package. (It was the idea behind the gun-control push, too, until a bipartisan background-check measure fell short in the Senate.)

“From a strategic standpoint, that’s probably a wise thing to do—try and get some sort of a bipartisan agreement reached on whatever the issue is,” said Sen. John Boozman, R-Ark. “If your conservative senator is voting for it, then that takes a lot of the pressure off the House members.”

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Major legislation passing one chamber with broad bipartisan majorities can be tough for the other chamber to simply ignore. “Bills that pass the Senate with significant numbers have an impact on the House,” said Sen. Roy Blunt, R-Mo., a member of the Senate leadership and a former House majority whip. “These probably will, too. But we’ll see if [Obama-backed measures] can get to significant numbers.”

The president has had little choice but to look to Senate Republicans as potential negotiating partners after House Speaker John Boehner declared a moratorium on any further one-on-one talks. It was no coincidence that Obama’s two GOP golf companions this week, Sens. Saxby Chambliss of Georgia and Bob Corker of Tennessee, have been among the Republicans most receptive to a grand budget accord that includes additional tax revenue.

But budget talks are likely to heat up only after votes on immigration, arguably the most important legacy issue for the second-term president. Two of the chief immigration-reform sponsors, Sens. John McCain, R-Ariz., and Chuck Schumer, D-N.Y., aim to run up the score, securing as many as 70 votes to force the House’s hand. Those two headed down Pennsylvania Avenue in mid-April to personally brief the president on their progress. They and the rest of the so-called Gang of Eight have asked Obama to give them some space to maneuver. “I would describe his role as just about perfect,” Schumer said of Obama at a recent joint breakfast with McCain. “I wouldn’t go that far,” McCain butted in.

The bank-shot strategy of propelling a measure so strongly through the Senate that the House must act does not guarantee success. Plenty of bills clear one chamber only to languish in the other. The fiscal-cliff accord that the White House sees as its model was unique: If the House didn’t act, taxes were going to rise on every American, and the GOP risked shouldering the blame. The pressure won’t be nearly as intense to pass immigration reform, say, or any other potential budget deal unless the country is on the precipice of default.

“No, not necessarily because it comes out of the Senate will the House take it up—or even take it seriously,” said Sen. Tim Scott, R-S.C., who served in the House last year and was close to leadership.

While Senate Democrats and the White House have been heartened by Boehner distancing himself from the “Hastert Rule,” which requires any bill on the floor to be backed by a majority of the majority, senior House Republicans say the president could be in for a rude awakening if and when his agenda is volleyed across the Capitol. “The administration seems to have a delusional belief that if they pick off a few Republicans and pass something in the Senate, it will magically pass the House,” a House Republican leadership aide said. “But that ain’t how things work under the American Constitution.”

The very same March day that the president visited the House GOP Conference, he spent the evening speaking to donors and volunteers for Organizing for Action, the political arm that grew out of his reelection campaign. Obama told the supporters he didn’t want to “repeat the mistake” of his first term and let them disperse. “When those voices are heard, you can’t stop it,” he said. “That’s when change happens.” The message House Republicans took from the dual appearances was clear: The president intends to try to browbeat them into submission.

But Republicans are mostly insulated in safe GOP districts. Only 17 House Republicans represent districts that Obama carried in 2012. “He may feel that revving up OFA and doing it the way they are doing is the way to go,” said Rep. Greg Walden, R-Ore., the chairman of the National Republican Congressional Committee. “I guess we’ll find out.”